Sparsistency for inverse optimal transport
Authors: Francisco Andrade, Gabriel Peyré, Clarice Poon
ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | This work presents an in-depth theoretical study of the ℓ1 regularization... As we illustrate in this theoretical article... This paper proposes the first mathematical analysis... Simple synthetic numerical explorations in Section 5.2 further provide intuition about how ε and the geometry of the graph associated with a sparse cost impact sparsistency. As a minor numerical contribution, we present in Appendix F a large-scale ℓ1-i OT solver, implemented in JAX and distributed as open-source software. Figure 1 illustrates how the value of the certificates zi,j evolves depending on the indexes (i, j) for three types of graphs... Figure 2 displays the recovery performances of ℓ1 i OT for the circular graph... These numerical simulations are obtained using the large-scale i OT solver, which we detail in Appendix F. |
| Researcher Affiliation | Academia | Francisco Andrade & Gabriel Peyré ENS Paris {francisco.andrade,gabriel.peyre}@ens.fr Clarice Poon University of Warwick clarice.poon@warwick.ac.uk |
| Pseudocode | No | The paper describes mathematical formulations and theoretical concepts related to optimal transport and inverse optimal transport, but it does not include any structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | As a minor numerical contribution, we present in Appendix F a large-scale ℓ1-i OT solver, implemented in JAX and distributed as open-source software. |
| Open Datasets | No | The numerical illustrations in Section 5.2 describe experiments with 'samples of Gaussian distributions' and set 'input measures as Σα = Σβ = Idn', indicating synthetic data generation rather than the use of a publicly available dataset with concrete access information (link, DOI, or formal citation). |
| Dataset Splits | No | The paper mentions using a 'number n of samples' for numerical simulations but does not provide specific details on how these samples are partitioned into training, validation, and test sets, nor does it reference any standard predefined splits. |
| Hardware Specification | No | The paper mentions numerical simulations and a solver used for them but does not provide any specific hardware details such as GPU models, CPU types, or cloud computing specifications used for running the experiments. |
| Software Dependencies | No | The paper states that the solver is 'implemented in JAX' in Appendix F, but it does not provide a specific version number for JAX or any other software dependencies, which is required for a reproducible description. |
| Experiment Setup | Yes | We fix the covariances of the input measures as Σα = Σβ = Idn... We consider that the support of the sought-after cost matrix A = δIdn +diag(G1n) G Rn n is defined as a shifted Laplacian matrix of some graph adjacency matrix G, for a graph of size n = 80... We set the shift δ to be 10% of the largest eigenvalue of the Laplacian... Figure 1 illustrates how the value of the certificates zi,j evolves depending on the indexes (i, j) for three types of graphs... for several values of ε. Figure 2 displays the recovery performances of ℓ1 i OT... as a function of λ for three different values of ε. |